Compound Probability Practice

Front

What is compound probability?

Back

Compound probability refers to the probability of two or more events happening at the same time. It can be calculated using the multiplication rule for independent events or the addition rule for mutually exclusive events.

Front

How do you calculate the probability of drawing two diamonds from a deck of cards without replacement?

Back

To calculate the probability of drawing two diamonds without replacement, use the formula: P(A and B) = P(A) * P(B|A). For example, P(drawing 1st diamond) = 13/52 and P(drawing 2nd diamond) = 12/51. Thus, P(drawing two diamonds) = (13/52) * (12/51) = 1/17.

Front

What is the probability of spinning a 3 and an A on two spinners?

Back

If each spinner has 4 outcomes, the total outcomes when spinning two spinners is 4 * 4 = 16. The probability of landing on a 3 and an A is 1/16.

Front

How do you find the probability of choosing a dark chocolate candy and then a caramel candy?

Back

The probability of choosing a dark chocolate candy first is 16/28. After eating it, the probability of choosing a caramel candy is 12/27. Thus, the combined probability is (16/28) * (12/27) = 16/63.

Front

What is the formula for calculating the probability of two events happening in sequence?

Back

The formula is P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of event B occurring after event A has occurred.

Front

What is the probability of drawing a green marble first and a red marble second without replacement?

Back

If there are 7 green and 13 red marbles in a jar of 20, the probability of drawing a green first is 7/20, and then the probability of drawing a red is 13/19. Thus, the combined probability is (7/20) * (13/19) = 7/38.

Front

What is the probability of rolling a 6 on a die and then rolling an odd number?

Back

The probability of rolling a 6 is 1/6. The probability of rolling an odd number (1, 3, or 5) is 3/6. Thus, the combined probability is (1/6) * (3/6) = 1/12.

Front

What is the difference between independent and dependent events in probability?

Back

Independent events are those where the outcome of one event does not affect the outcome of another (e.g., rolling a die). Dependent events are those where the outcome of one event affects the outcome of another (e.g., drawing cards without replacement).

Front

How do you calculate the probability of two independent events occurring?

Back

For independent events, the probability of both events occurring is the product of their individual probabilities: P(A and B) = P(A) * P(B).

Front

What is the total number of outcomes when rolling two dice?

Back

When rolling two dice, the total number of outcomes is 6 (for the first die) * 6 (for the second die) = 36.